A.E.Eiben, E.H.L.Aarts, and K.M. van Hee, \Global convergence of genetic algorithms: A Markov chain analysis," in Parallel Problem Solving from Nature, H.P.Schwefel and R.Manner, Eds. Berlin: Springer-Verlag, pp.4-12, 1991.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... un optimum global pour une grande classe de problemes d optimisation definis sur un ensemble discret [3] Des etudes theoriques ont demontre que sous certaines hypotheses de regularite pour la fonction force, ces algorithmes convergent asymptotiquement vers des solutions optimales globales ( cf. [4] ) L optimisation par AG de fonctions de IR dans IR necessite un codage des parametres reels en chane d entiers et entrane une forte complexite. D autres algorithmes evolutionnistes n utilisent pas de genotype. Les operateurs travaillent alors directement sur le phenotype qui peut avoir une ....

A. E. Eiben, E. H. L. Aaarts, and K. M. Van hee. Global Convergence of Genetic Algorithms: A Markov chain analysis. In H. P. Schwefel and Eds R. M anner, editors, Parallel Problem Solving from Nature, 1991.

....the future search. Successive dependence on the poor information would eventually cause the search to get stuckinthepoor local optimum. Hence, we employawell known strategy in evolutionary computation to pull the deceived population away from the wrong guidance. The strategy used is elitism (see [30,20,19, 18] for the importance of this strategy. which is a heuristic making use of the fittest individual found in the course of generations to guide the search. This heuristic is used with an assumption that the chance of finding a fitter elite is greater or equal at the region of the elite currently ....

A.E. Eiben, E.H.L. Aarts, and K.M. Van Hee. Global convergence of genetic algorithms: A markovchain analysis. In H.P.Schwefel and R. Manner, editors, Parallel Problem Solving from Nature, pages 4--12. Heidelberg,Berlin: Springer-Verlag, 1991.

....desirable to have some theoretical understanding of algorithm performance. A large portion of the literature on theoretical analysis of local search algorithms for other problems has been devoted to determining the convergence of search algorithms to the global optimum using Markov models [2] [3], 7] 8] 9] 11] The rates of convergence to the optimum have also been discussed assuming various properties of cost functions and search spaces [15] 16] Some work in the area of complexity theory has been focused on studying PLS (polynomial 2 Krishnamachari, Xie, Selman and Wicker ....

A.E. Eiben, E.H.L. Aarts, and K.M. Van Hee, \Global convergence of genetic algorithms: a markov chain analysis," Parallel Problem Solving from Nature, PPSN 1, p. 4-12, October 1990.

....to the populations that contain the optimum. But the deterministic decision of preserving the best tted individual seems to crack the idea of GAs as global random search algorithms. Elitism can be seen as an instance of a reduction operator. Reduction operators were introduced by Eiben et al. [5], where rather general conditions for convergence were discussed. In this work, a strong condition on the reduction operator was set to guarantee convergence: the reduction operator must be conservative (it must preserve the best tted individual) Our work in this paper shows that a probabilistic ....

....2 GA with Reduction Operator We propose an algorithm in which an iteration is composed by the application of selection, crossover, mutation and the reduction operator. The concrete form of the reduction operator is the main di erence between our approach and simple GAs, or the GA exposed in [5]. This operator depends on the temperature parameter which can change in each iteration of the algorithm. If we suppose that the size of the population for the algorithm is n, then a pseudo code for the algorithm can be seen in Fig. 1. In this algorithm we suppose that the selection is carried ....

A.E. Eiben, E.H.L. Aarts and K.M. Van Hee, Global convergence of genetic algorithms: A Markov chain analysis, in: Parallel Problem Solving from Nature, Lectures notes in computer science, Vol. 496 (1991), 4-12.

....using Markov chain analyses. Though considered a marginal operator in the GA paradigm [27, 22] the mutation operator is at the core of all convergence results obtained so far in that domain, responsible for the ergodicity of the Markov chain representing the evolutionary process: Early works [19, 17, 33, 45] consider simpli ed models; Rudolph convergence results [38] directly rely on the positivity 1 of the mutation operator, while their recent extension by Agapie [3] relaxes the strong hypothesis of positive mutations to the existence of a nite chain of mutations linking any two points of the ....

A.E. Eiben, E.H.L. Aarts, and K.M. Van Hee. Global convergence of genetic algorithms: a markov chain analysis. In Hans-Paul Schwefel and Reinhard Manner, editors, Proceedings of the 1 st Parallel Problem Solving from Nature, pages 4-12. Springer Verlag, 1991.

.... than schemata (predicates [39] formae [30, 31] interval for real coded individuals [13] Other works on the behavior of GAs focus on giving a proof of convergence of the algorithm, either by enhancing the schema theorem [43] 41, 26, 40] or by modeling the behavior of the GA with Markov s chain [11] [29] 8] A very interesting review of all these works is available in [27] Though interesting, it should be noted that all these works mostly tend to describe the process rather than explaining the way it works. In this sense, it is of too high level to fully understand the miscellaneous ....

A. E. Eiben, E. H. L. Aarts, and K. M. V. Hee. Global convergence of genetic algorithms: a markov chain analysis. In [36], pages 1--12, October 1991.

.... the entire transition matrix between population states be computed, they are only presently capable of being used to analyse very small search spaces (typically binary problems with no more than a few bits) Various Markov models of evolutionary algorithm behaviour have also been developed (e.g. Eiben et al. 1990; Davis Principe, 1993) but it is not clear how relevant these are to practical optimisation (limited to finite populations and finite time) A large body of work has also been generated from the study of deception , which essentially aims to understand what makes particular combinations of ....

A. E. Eiben, E. H. L. Aarts, and K. M. V. Hee, 1990. Global convergence of genetic algorithms: A markov chain analysis. In H. P. Schwefel and R. Manner, editors, Parallel Problem Solving From Nature, pages 4--12. Springer-Verlag.

....their strength; it allows different solutions to share information with each other. Some genetic algorithms are capable of varying the probability of allowing a solution to be replaced by one of lower quality. Such an algorithm can be viewed as a generalized simulated annealing algorithm [31]. However, unlike a classical simulated annealing algorithm, this sort of genetic algorithm simultaneously operates on multiple solutions which share information with each other. The genetic algorithm employed by MOGAC shares the strengths of classical genetic algorithms and simulated annealing ....

A. E. Eiben, E. H. L. Aarts, and K. M. V. Hee, "Global convergence of genetic algorithms: A Markov chain analysis," in Lecture Notes in Computer Science: Parallel Problem Solving from Nature, vol. 496, pp. 4--12, Springer-Verlag, Berlin, Germany, 1991.

....local search component corresponds to individual or ontogenetic learning. In contrast to nature, the artificial evolution also offers the possibility of inheriting the local search results as described by Lamarck. Viewing the sequence of generations produced by a GA as a Markov chain, Eiben et al. [7] examine the general GA characteristics that make GAs suitable to solve combinatorial optimization problems. They state some simple sufficient conditions under which a GA almost surely finds an optimum (i.e. finds an optimum with probability one within an infinite number of generations) The ....

Eiben, A.E., E.H.L. Aarts, and K.M. Van Hee (1990): Global convergence of genetic algorithms: A Markov chain analysis. Lecture Notes in Computer Science, Vol. 496, pp. 4-12.

.... Strategies allowed precise theoretical studies on the rate of convergence of these algorithms using probability calculus (at least for locally convex functions) Results based on Markov chains analysis are available for the standard GA scheme (proportional selection with fixed mutation rate) [43, 98]. The need for an elitist strategy is emphasized by Rudolph [116] When the mutation rate is allowed to decrease along generations, techniques borrowed from the field of Simulated Annealing give more precise convergence results in probability [34, 35] Yet a different approach is used by Cerf ....

A.E. Eiben, E.H.L. Aarts, and K.M. Van Hee. Global convergence of genetic algorithms: a markov chain analysis. In Hans-Paul Schwefel and Reinhard Manner, editors, Proceedings of the 1 st Parallel Problem Solving from Nature, pages 4--12. Springer Verlag, 1991.

....work on the foundations of genetic algorithms. There is much more work on the foundations of genetic algorithms, and also in the wider field of evolutionary computation, see for example [2,20] There are many interesting results (also for the finite case) for example based on Markov chains, cf. [6,16,19,20]. Acknowledgement We would like to thank Jeannette de Graaf, Adriaan Schippers and the anonymous referees for their helpful comments. ....

A.E. Eiben, E.H.L. Aarts and K.M. van Hee, Global convergence of genetic algorithms: A Markov chain analysis, in: H.-P. Schwefel and R. Manner, ed., Proceedings of the First Conference on Parallel Problem Solving from Nature, LNCS 496 (Springer-Verlag, Berlin, 1991) 4--12.

....minimal elements provided that the selection mechanism employs some kind of elitism and that the time invariant variation operator s support is identical to the search space. This result includes earlier established convergence results regarding single objective EAs with finite search space (e.g. [4 7]) as special cases. Moreover, it also includes a new convergence result for multi objective EAs. Section 4 is devoted to transcribe the general result into the terminology of these special cases. Finally, some directions towards an extension of the presented theory are discussed in Section 5. 2 ....

A. E. Eiben, E. H. L. Aarts, and K. M. Van Hee. Global convergence of genetic algorithms: A markov chain analysis. In H.-P. Schwefel and R. Manner, editors, Parallel Problem Solving from Nature, pages 4--12. Springer, Berlin and Heidelberg, 1991.

....only solvable instances are used in this research. As we work with CSPs and a solution is always forced to exist, we can compare the algorithms on the time that they need to find a solution. Theorems exist saying that some probabilistic algorithms are guaranteed to find a solution if one exists [20], but infinite time is needed to guarantee this and in practice we will need to define a maximum on the computational effort that an algorithm is allowed to take, so that not in all runs a solution will be found. As the results are averaged over multiple runs, a natural measure to compare ....

A.E. Eiben, E.H.L. Aarts, and K.M. van Hee. Global convergence of genetic algorithms: A markov chain analysis. In R. Manner and B. Manderick, editors, Proceedings of the 2nd Parallel Problem Solving from Nature, pages 4--12. North-Holland, 1992.

....function, and T is the temperature control parameter, then Boltzmann scaled fitness is given by the equation, F (x) e SigmaU (x) T , where the sign determines whether maximization or minimization is performed. Also worth mentioning is Eiben, Aarts, and Van Hee s abstract genetic algorithm [15], of which GAs and SA are special cases. Their theoretical view of the two algorithms is complementary to that presented here, specifically, that SA can be viewed as a special form of genetic algorithm characterized by populations of size 1 : where children are produced exclusively by ....

A. E. Eiben, E. H. L. Aarts, and K. M. Van Hee, Global convergence of genetic algorithms: a Markov chain analysis, Lecture Notes in Computer Science: Parallel Problem Solving from Nature 496 (1991) 4--12.

.... Strategies allowed precise theoretical studies on the rate of convergence of these algorithms using probability calculus (at least for locally convex functions) Results based on Markov chains analysis are available for the standard GA scheme (proportional selection with fixed mutation rate) [53, 124]. The need for an elitist strategy is emphasized by Rudolph [143] When the mutation rate is allowed to decrease along generations, techniques borrowed from the field of Simulated Annealing give more precise convergence results in probability [40, 41] Yet a different approach is used by Cerf ....

A.E. Eiben, E.H.L. Aarts, and K.M. Van Hee. Global convergence of genetic algorithms: a markov chain analysis. In Hans-Paul Schwefel and Reinhard Manner, editors, Proceedings of the 1 st Parallel Problem Solving from Nature, pages 4--12. Springer Verlag, 1991.

....each variant of an evolutionary algorithm in order to investigate the limit behavior. Instead, qualitative models are sufficient for this purpose. The idea to characterize the limit behavior of the evolutionary algorithm by the properties of the variation and selection operators was realized in [7]. This approach is adopted here. Actually, almost all results presented in this subsection are already given in [7, 8] Subsequent publications offered some minor 4 author short title extensions in case of specific combination of variation and selection operators [9, 10, 11, 12] or from a more ....

....are sufficient for this purpose. The idea to characterize the limit behavior of the evolutionary algorithm by the properties of the variation and selection operators was realized in [7] This approach is adopted here. Actually, almost all results presented in this subsection are already given in [7, 8]. Subsequent publications offered some minor 4 author short title extensions in case of specific combination of variation and selection operators [9, 10, 11, 12] or from a more abstract point of view [13, 14] In retrospective, one may say that the intensive elaboration of these issues during ....

A. E. Eiben, E. H. L. Aarts, and K. M. van Hee. Global convergence of genetic algorithms: A markov chain analysis. In H.-P. Schwefel and R. M¨anner, editors, Parallel Problem Solving from Nature, pages 4--12. Springer, Berlin and Heidelberg, 1991.

....is said to converge to the global optimum if it generates a sequence of solutions or function values in which the global optimum is a limit value. A probabilistic version of this definition is used in this paper. Markov chains offer an appropriate model to analyze GAs and they have been used in [2] and [3] to prove probabilistic convergence of the best solution within a population to the global optimum under elitist selection (the best individual survives with probability one) This paper analyzes the global convergence properties of the original CGA and modified versions that simply save ....

A.E. Eiben, E.H.L. Aarts, and K.M. Van Hee, "Global convergence of genetic algorithms: A markov chain analysis", in Parallel Problem Solving from Nature, H.-P. Schwefel and R. Manner (Eds.), Berlin and Heidelberg: Springer, 1991, pp. 4--12.

....operator, it allows a better exploration of the searching space and gives better findings. Some comparative results relative to the optimization of test functions taken from literature are given. Keywords: Convergence, Crossover, Genetic Algorithms. 1 Introduction Genetic Algorithms (GAs) [1 3] are a widely used optimization algorithm. They have high insensibility with respect to local minima and very fast starting convergence; they do not require the knowledge of the gradient of the function to optimize; they offer a large amount of large grain parallelism, so they can be efficiently ....

Eiben,A.E., Aarts,E.H.L. Van Hee,K.M : 'Global convergence of Genetic Algorithms: a Markov chain analysis' - Proceedings of the 1 st workshop on Parallel Problem Solving from Nature - Dortmund, West Germany, 1-3 October 1990

....a completely different one. In this way one obtains a heuristic based genetic algorithm (HGA) which is summarized in Figure 1. The above described simple genetic algorithm GA belongs to a class of genetic algorithms for which theoretical results on global convergence have been established (cf. [9, 27]) Notice that the integration of the HA procedure does not affect the global convergence properties of the GA. Concerning the computational complexity of the algorithm, it can be easily shown that the worst case complexity per iteration is O(N 2 ) where N is the number of nodes of the graph. ....

A.E. Eiben, E.H.L. Aarts, and K.M. Van Hee. Global convergence of genetic algorithms: a Markov chain analysis. In H.P. Schwefel and R. Manner, editors, Parallel Problem Solving from Nature, pages 4--12. Springer-Verlag, LNCS 496, 1991.

.... programming (EP) methods for parameter optimization [4] and elitist genetic algorithms (GA) as introduced in [5] Whenever the support of the invariant mutation distribution covers the feasible region of the optimization problem, it is easy to prove convergence to the global optimum [6] 7][8][4] for these algorithms. For non elitist EAs the conditions for convergence are more delicate: The standard GA as introduced in [9] does not converge at all regardless of the objective function and the choice of the crossover operator [10] But it can be shown that a standard GA is able to ....

A.E. Eiben, E.H.L. Aarts, and K.M. Van Hee. Global convergence of genetic algorithms: A markov chain analysis. In H.-P. Schwefel and R. M¨anner, editors, Parallel Problem Solving from Nature, pages 4--12. Springer, Berlin and Heidelberg, 1991.

....of an EA only depends on the state of the previous population in a probabilistic manner, it is clear that Markov chains are appropriate to model and analyze evolutionary algorithms. First theoretical results, basing on qualitative models, concerning the limit behavior of EAs were available in 1991 [18]. About the same time there appeared the first papers presenting the exact transition matrices of the Markov chains associated with certain evolutionary algorithms [19,20] Although the entire information about the evolutionary process is contained in these transition matrices, the degree of ....

A. E. Eiben, E. H. L. Aarts, and K. M. Van Hee. Global convergence of genetic algorithms: A markov chain analysis. In H.-P. Schwefel and R. Manner, editors, Parallel Problem Solving from Nature, pages 4--12. Springer, Berlin and Heidelberg, 1991.

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A.E.Eiben, E.H.L.Aarts, and K.M. van Hee, \Global convergence of genetic algorithms: A Markov chain analysis," in Parallel Problem Solving from Nature, H.P.Schwefel and R.Manner, Eds. Berlin: Springer-Verlag, pp.4-12, 1991.

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A.E.Eiben, E.H.L.Aarts, and K.M. van Hee, "Global convergence of genetic algorithms: A Markov chain analysis," in Parallel Problem Solving from Nature, H.P.Schwefel and R.Manner, Eds. Berlin: Springer-Verlag, pp.4-12, 1991.

No context found.

A.E. Eiben, E.H.L. Aarts, and K.M. Van Hee, \Global convergence of genetic algorithms: a markov chain analysis," Parallel Problem Solving from Nature, PPSN 1, p. 4-12, October 1990.

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Eiben, A. E., Aarts, E. H. L., and Van Hee, K. M. (1991). Global convergence of genetic algorithms: a markov chain analysis. In Schwefel, H.-P. and Manner, R., editors, Proceedings of the 1 st Parallel Problem Solving from Nature, pages 4-12, Springer Verlag, Berlin.

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